Fire Hero
In Suikoden II, if you go to Tigermouth village you can find a man there that talks about the "Fire Hero". In Suikoden III he's called "Flame Champion" instead.
Versions: NTSC UC
Prince Luca
Luca Blight is the Prince of Highland, later becoming the King. In Suikoden III's book about the Dunan Unification War he's been promoted to Emperor instead!
Versions: NTSC UC
Gustav
Gustav plays a semi-big part in Suikoden II, for this effort he was rewarded with name change to Gustaf in Suikoden III.
Versions: NTSC UC
Howling Voice Guild
The Howling Voice has a quick appearance in Suikoden III, though Konami decided to call them the Roaring Brotherhood instead.
Versions: NTSC UC
Keepers of the Flame
If you read the book about the Grasslands in Suikoden II you will come across the "Keepers of the Flame". In Suikoden III they have apparently been reduced to 1 person called the "Fire Bringer"
Versions: NTSC UC
Rune Master
In Suikoden II they're called "Rune Masters", in Suikoden III they're "Rune Sages" instead.
Versions: NTSC UC
Sindar
In Suikoden II it's spelled Sindar. In Suikoden III it's changed to Cyndar.
Versions: NTSC UC